Other tags that relate to Starfish Spotting
Generalising. Games. Multiplication & division. Addition & subtraction. Factors and multiples. Describing patterns and sequences. Working systematically. Combinations. Trial and improvement. Investigations.There are 92 results
Broad Topics > Thinking Mathematically > Generalising
Doplication
Age 7 to 11
Challenge Level
We can arrange dots in a similar way to the 5 on a dice and they usually sit quite well into a rectangular shape. How many altogether in this 3 by 5? What happens for other sizes?
Magic Constants
Age 7 to 11
Challenge Level
In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?
Centred Squares
Age 7 to 11
Challenge Level
This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.
Calendar Calculations
Age 7 to 11
Challenge Level
Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?
The Add and Take-away Path
Age 5 to 7
Challenge Level
Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?
Journeys in Numberland
Age 7 to 11
Challenge Level
Tom and Ben visited Numberland. Use the maps to work out the number of points each of their routes scores.
Broken Toaster
Age 7 to 11 Short
Challenge Level
Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?
Button-up Some More
Age 7 to 11
Challenge Level
How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?
Number Differences
Age 7 to 11
Challenge Level
Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?
Growing Garlic
Age 5 to 7
Challenge Level
Ben and his mum are planting garlic. Can you find out how many cloves of garlic they might have had?
Lots of Lollies
Age 5 to 7
Challenge Level
Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?
Polygonals
Age 7 to 11
Challenge Level
Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.
Number Tracks
Age 7 to 11
Challenge Level
Ben’s class were cutting up number tracks. First they cut them into twos and added up the numbers on each piece. What patterns could they see?
Unit Differences
Age 5 to 7
Challenge Level
This challenge is about finding the difference between numbers which have the same tens digit.
Sitting Round the Party Tables
Age 5 to 11
Challenge Level
Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.
Sums and Differences 2
Age 7 to 11
Challenge Level
Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?
Lost Books
Age 7 to 11
Challenge Level
While we were sorting some papers we found 3 strange sheets which seemed to come from small books but there were page numbers at the foot of each page. Did the pages come from the same book?
Digit Addition
Age 5 to 11
Challenge Level
Try out this number trick. What happens with different starting numbers? What do you notice?
Sums and Differences 1
Age 7 to 11
Challenge Level
This challenge focuses on finding the sum and difference of pairs of two-digit numbers.
Build it Up
Age 7 to 11
Challenge Level
Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.
Build it up More
Age 7 to 11
Challenge Level
This task follows on from Build it Up and takes the ideas into three dimensions!
Bundles of Cubes
Age 7 to 11
Challenge Level
Watch this animation. What do you notice? What happens when you try more or fewer cubes in a bundle?
Magic Circles
Age 7 to 11
Challenge Level
Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?
Making Maths: Be a Mathemagician
Age 7 to 11
Challenge Level
Surprise your friends with this magic square trick.
Oddly
Age 7 to 11
Challenge Level
Find the sum of all three-digit numbers each of whose digits is odd.
Division Rules
Age 7 to 11
Challenge Level
This challenge encourages you to explore dividing a three-digit number by a single-digit number.
Strike it Out
Age 5 to 11
Challenge Level
Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.
The Great Tiling Count
Age 7 to 11
Challenge Level
Compare the numbers of particular tiles in one or all of these three designs, inspired by the floor tiles of a church in Cambridge.
Area and Perimeter
Age 7 to 11
Challenge Level
What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.
Magic Vs
Age 7 to 11
Challenge Level
Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?
Tiling
Age 7 to 11
Challenge Level
An investigation that gives you the opportunity to make and justify predictions.
Round and Round the Circle
Age 7 to 11
Challenge Level
What happens if you join every second point on this circle? How about every third point? Try with different steps and see if you can predict what will happen.
Charitable Pennies
Age 7 to 14
Challenge Level
Investigate the different ways that fifteen schools could have given money in a charity fundraiser.
Dice Stairs
Age 7 to 11
Challenge Level
Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?
Sticky Triangles
Age 7 to 11
Challenge Level
Can you continue this pattern of triangles and begin to predict how many sticks are used for each new "layer"?
Strike it Out for Two
Age 5 to 11
Challenge Level
Strike it Out game for an adult and child. Can you stop your partner from being able to go?
Steps to the Podium
Age 7 to 14
Challenge Level
It starts quite simple but great opportunities for number discoveries and patterns!
Truth or Lie
Age 7 to 11
Challenge Level
Take a look at the video of this trick. Can you perform it yourself? Why is this maths and not magic?
Next-door Numbers
Age 5 to 7
Challenge Level
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
More Numbers in the Ring
Age 5 to 7
Challenge Level
If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?
Play to 37
Age 7 to 11
Challenge Level
In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.
Round the Three Dice
Age 7 to 11
Challenge Level
What happens when you round these three-digit numbers to the nearest 100?
What Could it Be?
Age 5 to 7
Challenge Level
In this calculation, the box represents a missing digit. What could the digit be? What would the solution be in each case?
Stop the Clock for Two
Age 5 to 7
Challenge Level
Stop the Clock game for an adult and child. How can you make sure you always win this game?
Cuisenaire Squares
Age 7 to 11
Challenge Level
These squares have been made from Cuisenaire rods. Can you describe the pattern? What would the next square look like?
Surprising Split
Age 7 to 11
Challenge Level
Does this 'trick' for calculating multiples of 11 always work? Why or why not?
How Odd
Age 5 to 7
Challenge Level
This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?
Winning Lines
Age 7 to 16
An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.
NRICH is part of the family of activities in the Millennium Mathematics Project.